Presenter: Zeng Fanhai
We develop two fast methods, Fast Method I and Fast Method II, with linear complexity to calculate the discrete convolution for the approximation of the fractional operator. Fast Method I is based on a local approximation for the contour integral that represents the convolution weight. Fast Method II is based on a globally uniform approximation of the trapezoidal rule for the integral on the real line. Both methods are efficient, but numerical experimentation reveals that Fast Method II outperforms Fast Method I in terms of accuracy, efficiency, and coding simplicity for dealing the fractional derivative operator. The memory requirement and computational cost of Fast Method II are O(Q) and O(QnT), respectively, where nT is the number of the final time steps and Q is the number of quadrature points used in the trapezoidal rule. The effectiveness of the fast methods is verified through a series of numerical examples for long-time integration, including a numerical study of a fractional reaction-diffusion model.
Brief Introduction to the Presenter:
After graduation, Doctor Zeng was committed to his postdoctoral research in Brown University in the United States, Queensland University of Technology in Australia and National University of Singapore successively, published more than ten academic papers in the first-class journals of computational mathematics such as SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics, etc., co-published a monograph, and thereby making some influential contributions to the singularity processing of non-local-problem numerical method and the field of fast algorithm, whose 7 ESI papers are cited at a super high frequency with the highest citation rate of a single paper reaching 131 times. In 2016, he won the Shanghai Excellent Doctoral Dissertation Award.
Jiang Xiaoyun, Professor of the School of Mathematics, Shandong University
10:00-11:00, December 8 (Sunday)
Lecture Hall 1238, Block B, Zhixin Building, Central Campus
Sponsored by: School of Mathematics, Shandong University